"No. Why stop the user from copy-pasting their own password?
Whenever you're looking at a security protection like this, it's important to ask yourself: Exactly what kind of attacks are am I trying to protect against? In this case, even if you prevent copy-paste, the user can just retype it if they really want to, after all. And if you're worried about Evil Spyware, that stuff can just install a browser extension and look at the password in the DOM directly, or install a keylogger and capture it as it's being typed.
Indeed, this can even reduce security. Consider if the user's using a password management program that can either put the password into the clipboard, or display it for retyping. If you prevent paste, that means the user must display the password on screen for any shoulder surfers to see."